Long flows contribute huge volumes of traffic over inter-datacenter WAN. The Flow Completion Time (FCT) is a vital network performance metric that affects the running time of distributed applications and the users quality of experience. Flow routing techniques based on propagation or queuing latency or instantaneous link utilization are insufficient for minimization of the long flows FCT. We propose a routing approach that uses the remaining sizes and paths of all ongoing flows to minimize the worst-case completion time of incoming flows assuming no knowledge of future flow arrivals. Our approach can be formulated as an NP-Hard graph optimization problem. We propose BWRH, a heuristic to quickly generate an approximate solution. We evaluate BWRH against several real WAN topologies and two different traffic patterns. We see that BWRH provides solutions with an average optimality gap of less than $0.25%$. Furthermore, we show that compared to other popular routing heuristics, BWRH reduces the mean and tail FCT by up to $1.46times$ and $1.53times$, respectively.
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